Sublation [Aufhebung], as I understand it, is Hegel's term for the process by which a state is "raised up," or cancelled out into a new, higher state of being. So in Hegel's system, history unfolds as an optimistic, progressive movement toward the revelation of absolute spirit in the world. It's a kind of optimism that been co-opted (knowingly or not) by all sorts of groups in contemporary culture - from those of us who think science is progressively discovering more and more about the world and will ultimately explain everything[1]to people who think that humanity is just getting better and that the world is generally improving (the "up and to the right" thinkers, as they say in economics). In other words, history is a progression from state to (higher) state without looking back - "without remainder."

But Hegel adds a wrinkle to Aufhebung which not everyone acknowledges. In the Science of Logic Hegel is very clear about it however:

The German “aufheben” (“to sublate” in English) has a twofold meaning in the language: it equally means “to keep,” “to ‘preserve’,” and “to cause to cease,” “to put an end to.” Even “to preserve” already includes a negative note, namely that something, in order to be retained, is removed from its immediacy and hence from an existence which is open to external influences. – That which is sublated is thus something at the same time preserved, something that has lost its immediacy but has not come to nothing for that. – These two definitions of “to sublate” can be cited as two dictionary meanings of the word. But it must strike one as remarkable that a language has come to use one and the same word for two opposite meanings. For speculative thought it is gratifying to find words that have in themselves a speculative meaning.[2]

So sublation is a speculative term for Hegel, which means that it "disputes itself." Thus, when something is sublated it is not annulled or cancelled out; it remains as an element in the new state, which means that there can never be a clean break between states. Hegel may arbitrarily posit a linear progression from A to B to C etc., but this can never be guaranteed because of the very mechanism of sublation he uses.

Footnotes

^I think this includes people who think we are free to pollute the planet as much as we want because, hey, by the time the Earth becomes uninhabitable we'll just build huge spaceships and go off to colonize other planets Battlestar-Galactica style!